Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations Article Swipe

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Xiaoying Dai , Yan Pan , Bin Yang Bin Yang , Aihui Zhou ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.4208/aamm.oa-2023-0099

In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity.

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Estimator Mathematics Eigenvalues and eigenvectors A priori and a posteriori Rate of convergence Discretization Convergence (economics) Applied mathematics Mathematical optimization Computer science Mathematical analysis Key (lock) Physics Computer security Economics Philosophy Quantum mechanics Statistics Epistemology Economic growth

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Type: article
Language: en
Landing Page: https://doi.org/10.4208/aamm.oa-2023-0099
PDF: https://global-sci.org/intro/online/preview?online_id=2160&pdf=https://doc.global-sci.org/uploads/admin/article_pdf/20231222/2a25007c3addce3bf7811d7d2313c0f8.pdf
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DOI: https://doi.org/10.4208/aamm.oa-2023-0099

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Title: Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

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Authors: Xiaoying Dai, Yan Pan, Bin Yang Bin Yang, Aihui Zhou

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Concepts: Estimator, Mathematics, Eigenvalues and eigenvectors, A priori and a posteriori, Rate of convergence, Discretization, Convergence (economics), Applied mathematics, Mathematical optimization, Computer science, Mathematical analysis, Key (lock), Physics, Computer security, Economics, Philosophy, Quantum mechanics, Statistics, Epistemology, Economic growth

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